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A210212 Triangle of coefficients of polynomials v(n,x) jointly generated with A210211; see the Formula section. 3
1, 2, 2, 3, 5, 4, 4, 10, 11, 8, 5, 16, 28, 23, 16, 6, 24, 51, 72, 47, 32, 7, 33, 90, 144, 176, 95, 64, 8, 44, 138, 294, 377, 416, 191, 128, 9, 56, 208, 492, 878, 938, 960, 383, 256, 10, 70, 290, 830, 1577, 2462, 2251, 2176, 767, 512, 11, 85, 400, 1250, 2952 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First and last terms of row n: n and 2^(n-1)

Alternating row sums are signed products of two Fibonacci numbers.

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..60.

FORMULA

u(n,x)=x*u(n-1,x)+v(n-1,x)+1,

v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

EXAMPLE

First five rows:

1

2...2

3...5...4

4...10...11...8

5...16...28...23...16

First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 4x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;

v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;

Table[Expand[u[n, x]], {n, 1, z/2}]

Table[Expand[v[n, x]], {n, 1, z/2}]

cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

TableForm[cu]

Flatten[%]    (* A210211 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A210212 *)

CROSSREFS

Cf. A210211, A208510.

Sequence in context: A282443 A210554 A208912 * A209762 A026408 A301790

Adjacent sequences:  A210209 A210210 A210211 * A210213 A210214 A210215

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 19 2012

STATUS

approved

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Last modified October 19 03:31 EDT 2019. Contains 328211 sequences. (Running on oeis4.)